E (xf) X = 19.7 n E(x – x)²f - S = 19.8 п — 1 Grouped Frequency Distribution for Example 19.2 TABLE 19. 1 Scores Range Frequency 58, 53, 56 50-59 68, 60, 62, 65, 62 60-69 75, 75, 78, 73, 70, 70, 75, 72, 79 70–79 9. 80, 85, 88, 83, 85, 87 80-89 95, 97, 90 90-99 3 3.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The scores of a test for an engineering class of 30 students are shown here. Organize the data in a manner similar to Table 19.1 and
use Excel to create a histogram.
Scores: 57, 94, 81, 77, 66, 97, 62, 86, 75, 87, 91, 78, 61, 82, 74, 72, 70, 88, 66, 75, 55, 66, 58, 73, 79, 51, 63, 77, 52, 84
Using Equations (19.7) and (19.8) , calculate the mean and standard deviation of the class scores.
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